{"id":4124,"date":"2022-03-24T20:50:47","date_gmt":"2022-03-24T20:50:47","guid":{"rendered":"https:\/\/stage-wp.10minuteschool.com\/?p=4124"},"modified":"2022-03-24T15:14:32","modified_gmt":"2022-03-24T15:14:32","slug":"gravitational-law-for-sphere","status":"publish","type":"post","link":"https:\/\/10minuteschool.com\/content\/gravitational-law-for-sphere\/","title":{"rendered":"\u0997\u09cb\u09b2\u0995\u09c7\u09b0 \u099c\u09a8\u09cd\u09af \u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7\u09c0\u09af\u09bc \u09b8\u09c2\u09a4\u09cd\u09b0\u09c7\u09b0 \u09ac\u09cd\u09af\u09ac\u09b9\u09be\u09b0 (Use of Gravitational law for sphere)"},"content":{"rendered":"

\u09a8\u09bf\u09b0\u09c7\u099f \u0997\u09cb\u09b2\u0995\u09c7\u09b0 \u0985\u09ad\u09cd\u09af\u09a8\u09cd\u09a4\u09b0\u09c7 \u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7\u09c0\u09af\u09bc \u09b8\u09c2\u09a4\u09cd\u09b0\u09c7\u09b0 \u09ac\u09cd\u09af\u09ac\u09b9\u09be\u09b0 :\u09ac\u09bf\u09ad\u09ac \u0993 \u09aa\u09cd\u09b0\u09be\u09ac\u09b2\u09cd\u09af \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc\u00a0 (<\/b>Uses of Gravitational law inside a solid sphere :Determination of potential and intensity)<\/b>\u00a0<\/b><\/h2>\n

\u00a0\u09af\u0996\u09a8 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u099f\u09bf \u0997\u09cb\u09b2\u0995\u09c7\u09b0 \u09ad\u09c7\u09a4\u09b0 \u0985\u09ac\u09b8\u09cd\u09a5\u09bf\u09a4:\u00a0<\/strong><\/h3>\n

\"gravitational-law\"<\/p>\n

\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf <\/span>P<\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u099f\u09bf \u0997\u09cb\u09b2\u0995\u09c7\u09b0 \u0989\u09aa\u09be\u09a6\u09be\u09a8\u09c7\u09b0 \u09ad\u09c7\u09a4\u09b0 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0 \u09b9\u09a4\u09c7 \u09a6\u09c2\u09b0\u09c7 \u0985\u09ac\u09b8\u09cd\u09a5\u09bf\u09a4 \u0964 <\/span>O<\/span>-\u0995\u09c7 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0 \u0995\u09b0\u09c7\u0964 \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7\u09c7\u09b0 \u0964 \u098f\u0995\u099f\u09bf \u0997\u09cb\u09b2\u0995 \u0986\u0981\u0995\u09be \u09b9\u09b2\u09cb\u0964 \u09ac\u09b2\u09be \u09af\u09be\u09af\u09bc, \u09b8\u09ae\u0997\u09cd\u09b0 \u0997\u09cb\u09b2\u0995\u099f\u09bf \u09a6\u09c1\u099f\u09bf \u0997\u09cb\u09b2\u0995\u09c7\u09b0 \u09af\u09cb\u0997\u09ab\u09b2 \u098f\u0995\u099f\u09bf \u09b9\u09b2\u09cb \u0964\u00a0 a \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7\u09c7\u09b0 \u09a8\u09bf\u09b0\u09c7\u099f \u0997\u09cb\u09b2\u0995 \u098f\u09ac\u0982 \u0985\u09aa\u09b0\u099f\u09bf <\/span>(a\u2013r) <\/span>\u00a0<\/span>\u09ac\u09c7\u09a7\u09c7\u09b0 \u09ab\u09be\u0981\u09aa\u09be \u0997\u09cb\u09b2\u0995\u0964 \u09a8\u09bf\u09b0\u09c7\u099f \u0997\u09cb\u09b2\u0995\u09c7\u09b0 \u09a6\u09b0\u09c1\u09a8 <\/span>P<\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7 \u09b8\u09c2\u09a4\u09cd\u09b0<\/a> \u09aa\u09cd\u09b0\u09af\u09bc\u09cb\u0997 \u0995\u09b0\u09c7 \u09aa\u09be\u0987,<\/span><\/p>\n

\u09ac\u09bf\u09ad\u09ac, \\left(V_{p}\\right)_{1} <\/span><\/span>=-\\frac{G M}{r} <\/span><\/span>=<\/span>–\\frac{-G \\frac{4}{3} \\pi r^{3} \\rho}{r} <\/span><\/span>=-\\frac{4}{3} \\pi \\rho G r^{2} <\/span><\/span><\/p>\n

\u098f\u0996\u09be\u09a8\u09c7, <\/span>M=<\/span> \u0997\u09cb\u09b2\u0995\u09c7\u09b0 \u09ad\u09b0 <\/span>=\\frac{4}{3} <\/span>\\pi r^{3} <\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \\rho <\/span><\/span>=<\/span> \u0989\u09aa\u09be\u09a6\u09be\u09a8\u09c7\u09b0 \u0998\u09a8\u09a4\u09cd\u09ac \u0964\u00a0\u00a0<\/span><\/p>\n

\u0986\u09ac\u09be\u09b0 <\/span>(a\u2013r) <\/span>\u00a0<\/span>\u09ac\u09c7\u09a7\u09c7\u09b0 \u09ab\u09be\u0981\u09aa\u09be \u0997\u09cb\u09b2\u0995\u099f\u09bf\u0995\u09c7 <\/span>x <\/span><\/span> \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7\u09c7\u09b0 \u098f\u09ac\u0982 <\/span>dx <\/span><\/span> \u09ac\u09c7\u09a7\u09c7\u09b0 \u0985\u09a8\u09c7\u0995\u0997\u09c1\u09b2\u09bf \u09aa\u09be\u09a4\u09b2\u09be \u0996\u09b2\u0995\u09c7\u09b0 \u09b8\u09ae\u09b7\u09cd\u099f\u09bf \u09ad\u09be\u09ac\u09be \u09af\u09c7\u09a4\u09c7 \u09aa\u09be\u09b0\u09c7\u0964 \u098f\u09b0\u0995\u09ae \u098f\u0995\u099f\u09bf \u0996\u09cb\u09b2\u0995\u09c7\u09b0 \u09a6\u09b0\u09c1\u09a8 \u0996\u09cb\u09b2\u0995\u09c7\u09b0 \u09ad\u09c7\u09a4\u09b0\u09c7\u09b0 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 <\/span>P<\/span> \u09a4\u09c7 \u09ac\u09bf\u09ad\u09ac<\/span><\/p>\n

\\left(d V_{p}\\right)_{2} <\/span>=\\frac{G 4 \\pi x^{2} d x \\rho}{x} <\/span><\/span>=-4 \\pi G \\rho x d x <\/span><\/span><\/p>\n

(a-r) <\/span><\/span> \u09ac\u09c7\u09a7\u09c7\u09b0 \u09b8\u09ae\u0997\u09cd\u09b0 \u0997\u09cb\u09b2\u0995\u09c7\u09b0 \u09a6\u09b0\u09c1\u09a8 \u09ac\u09bf\u09ad\u09ac,<\/span><\/p>\n

\\left(V_{p}\\right)_{2} <\/span>=-4 \\pi G \\rho <\/span>\\int_{r}^{a} x d x <\/span><\/span>==-2 \\pi G \\rho <\/span>\\left(a^{2}-r^{2}\\right) <\/span>\u00a0<\/span><\/p>\n

\u09a4\u09be\u09b9\u09b2\u09c7 \u09b8\u09ae\u0997\u09cd\u09b0 \u09a8\u09bf\u09b0\u09c7\u099f \u0997\u09cb\u09b2\u0995\u09c7\u09b0 \u09a6\u09b0\u09c1\u09a8 P \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09b0 \u09ac\u09bf\u09ad\u09ac,\u00a0<\/span><\/p>\n

\\left(V_{p}\\right)_{t} <\/span>=\\left(V_{p}\\right)_{1} <\/span><\/span>+\\left(V_{p}\\right)_{2} <\/span><\/span><\/p>\n

=-\\frac{4}{3} \\pi <\/span>G \\rho r^{2}<\/span><\/span>–2 \\pi <\/span>G \\rho\\left(a^{2}-r^{2}\\right) <\/span><\/span>=-2 \\pi G <\/span>\\rho\\left(\\frac{2}{3} r^{2}+a^{2}-r^{2}\\right) <\/span><\/span><\/p>\n

=-2 \\pi G \\rho <\/span>\\left(a^{2}-\\frac{r^{2}}{3}\\right) <\/span><\/span>=-2 \\pi G<\/span>\\frac{M}{\\frac{4}{3} \\pi a^{2}} <\/span>(a^{2}-\\frac{r^{2}}{3}) <\/span>(<\/span>\u2235\\rho <\/span>=\\frac{M}{V} <\/span><\/span>=\\frac{M}{\\frac{4}{3} \\pi a^{3}} <\/span>)<\/span><\/p>\n

\u2234\\left(V_{p}\\right)_{t} <\/span><\/span>=<\/span>-\\frac{-3 G M}{2 a^{3}} <\/span>(a^{2}-\\frac{r^{2}}{3} <\/span>)<\/span><\/p>\n

\u098f\u09ac\u0982 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0 \u09aa\u09cd\u09b0\u09be\u09ac\u09b2\u09cd\u09af,<\/span><\/p>\n

\\left(E_{p}\\right)_{t} <\/span>=\\frac{d}{d r} <\/span>\\left(V_{p}\\right)\u00a0<\/span>=\\frac{d}{d r} \u00a0<\/span>\\left(V_{p}\\right)_{t} <\/span>=\\frac{3 G M}{2 a^{3}} <\/span>x\\frac{2 r}{3} <\/span><\/span><\/p>\n

\u2234\\left(E_{p}\\right)_{t}<\/span><\/span>=\\frac{G M}{a^{3}} r <\/span><\/span><\/p>\n

\u09a8\u09bf\u09b0\u09c7\u099f \u0997\u09cb\u09b2\u0995\u09c7\u09b0 \u09ac\u09be\u0987\u09b0\u09c7 \u0995\u09cb\u09a8\u09cb \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7 \u09b8\u09c2\u09a4\u09cd\u09b0\u09c7\u09b0 \u09ac\u09cd\u09af\u09ac\u09b9\u09be\u09b0 :\u09ac\u09bf\u09ad\u09ac \u0993 \u09aa\u09cd\u09b0\u09be\u09ac\u09b2\u09cd\u09af \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc)<\/b> (<\/b>Use of gravitational law outside the sphere :Determination of potential and intensity)<\/b><\/h2>\n

\u09af\u0996\u09a8 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u099f\u09bf \u0997\u09cb\u09b2\u0995\u09c7\u09b0 \u09ac\u09be\u0987\u09b0\u09c7 \u0985\u09ac\u09b8\u09cd\u09a5\u09bf\u09a4:\u00a0<\/strong><\/h3>\n

\u00a0\u099a\u09bf\u09a4\u09cd\u09b0\u09be\u09a8\u09c1\u09af\u09be\u09af\u09bc\u09c0 <\/span>a<\/span> \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7 \u098f\u09ac\u0982 <\/span>M<\/span> \u09ad\u09b0\u09c7\u09b0 \u09a8\u09bf\u09b0\u09c7\u099f \u0997\u09cb\u09b2\u0995\u09c7\u09b0 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0 <\/span>O<\/span> \u09b9\u09a4\u09c7 <\/span>r<\/span> \u09a6\u09c2\u09b0\u09c7 \u0997\u09cb\u09b2\u0995\u09c7\u09b0 \u09ac\u09be\u0987\u09b0\u09c7 <\/span>P<\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u00a0 \u0985\u09ac\u09b8\u09cd\u09a5\u09bf\u09a4\u0964 \u09b8\u09ae\u0997\u09cd\u09b0 \u0997\u09cb\u09b2\u0995\u099f\u09bf\u0995\u09c7 x<\/span><\/span>\u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7\u09c7\u09b0 \u098f\u09ac\u0982 <\/span>dx <\/span><\/span> \u09ac\u09c7\u09a7\u09c7\u09b0 \u0985\u09a8\u09c7\u0995\u0997\u09c1\u09b2\u09cb \u09b8\u09ae\u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0\u09bf\u0995 \u09aa\u09be\u09a4\u09b2\u09be \u0996\u09cb\u09b2\u0995\u09c7\u09b0 \u09b8\u09ae\u09b7\u09cd\u099f\u09bf \u09ad\u09be\u09ac\u09be \u09af\u09c7\u09a4\u09c7 \u09aa\u09be\u09b0\u09c7\u0964<\/span><\/p>\n

\u0997\u09cb\u09b2\u0995\u099f\u09bf\u09b0 \u09ad\u09b0 dm<\/span><\/span>=4 \\pi r^{2} d x \\rho <\/span><\/span>,\u00a0<\/span> \u098f\u0996\u09be\u09a8\u09c7 <\/span>\u03c1<\/span>=<\/span> \u0989\u09aa\u09be\u09a6\u09be\u09a8\u09c7\u09b0 \u0998\u09a8\u09a4\u09cd\u09ac\u0964 <\/span>dm<\/span><\/span>\u0995\u09c7 <\/span>O<\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0\u09c0\u09ad\u09c2\u09a4 \u09ad\u09be\u09ac\u09be \u09af\u09c7\u09a4\u09c7 \u09aa\u09be\u09b0\u09c7\u0964 \u09b8\u09c1\u09a4\u09b0\u09be\u0982 <\/span>P<\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u098f\u09b0 \u09a6\u09b0\u09c1\u09a8 \u09ac\u09bf\u09a8\u09cd\u09a7\u09c1\u09a4\u09c7 \u09ac\u09bf\u09ad\u09ac, d V_{p} <\/span><\/span>=-\\frac{G d m}{r} <\/span><\/span><\/p>\n

\u098f\u09ac\u0982 \u09b8\u09ae\u0997\u09cd\u09b0 \u0997\u09cb\u09b2\u0995\u09c7\u09b0 \u09a6\u09b0\u09c1\u09a8 <\/span>P<\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09ac\u09bf\u09ad\u09ac, \\left(V_{p}\\right)_{0} <\/span><\/span>=\\frac{-G \\sum d m}{r} <\/span>=\\frac{-G M}{r} <\/span><\/span><\/p>\n

\u098f\u09ac\u0982 \u09aa\u09cd\u09b0\u09be\u09ac\u09b2\u09cd\u09af \\left(E_{p}\\right)_{0} <\/span><\/span>=-\\frac{d}{d r}<\/span>\\left(\\frac{-G M}{r}\\right)<\/span>=+\\frac{G M}{r^{2}} <\/span> <\/span>\"gravitational-law\"<\/p>\n

\u09af\u0996\u09a8 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u099f\u09bf \u0997\u09cb\u09b2\u0995\u09c7\u09b0 \u09aa\u09c3\u09b7\u09cd\u09a0\u09c7\u09b0 \u0989\u09aa\u09b0 \u0985\u09ac\u09b8\u09cd\u09a5\u09bf\u09a4:<\/strong>\u00a0<\/span><\/h3>\n

\u00a0\u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u09c7 <\/span>r=a<\/span> \u09ac\u09b8\u09bf\u09af\u09bc\u09c7 \u09aa\u09be\u0987,<\/span><\/p>\n

\u09ac\u09bf\u09ad\u09ac \\left(V_{p}\\right)_{0} <\/span><\/span>=-\\frac{G M}{a^{2}} <\/span><\/span><\/p>\n

\u098f\u09ac\u0982 \u09aa\u09cd\u09b0\u09be\u09ac\u09b2\u09cd\u09af \\left(E_{p}\\right)_{0} <\/span><\/span>=+\\frac{G M}{a^{2}} <\/span><\/span><\/p>\n

\u09ab\u09be\u0981\u09aa\u09be \u0997\u09cb\u09b2\u0995\u09c7\u09b0 \u09ac\u09be\u0987\u09b0\u09c7 \u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7\u09c0\u09af\u09bc \u09b8\u09c2\u09a4\u09cd\u09b0\u09c7\u09b0 \u09ac\u09cd\u09af\u09ac\u09b9\u09be\u09b0 :\u09ac\u09bf\u09ad\u09ac \u0993 \u09aa\u09cd\u09b0\u09be\u09ac\u09b2\u09cd\u09af \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc (\u00a0 \u00a0 <\/b>Use of gravitational law outside the hollow sphere :Determination of potential and intensity)<\/b>\u00a0<\/b><\/h2>\n

\u09af\u0996\u09a8 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u099f\u09bf \u0997\u09cb\u09b2\u0995\u09c7\u09b0 \u09ac\u09be\u0987\u09b0\u09c7 \u0985\u09ac\u09b8\u09cd\u09a5\u09bf\u09a4:<\/strong><\/h3>\n

\"gravitational-law\"<\/p>\n

\u00a0\u099a\u09bf\u09a4\u09cd\u09b0\u09c7 \u09ab\u09be\u0981\u09aa\u09be \u0997\u09cb\u09b2\u0995\u09c7\u09b0 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0 <\/span>O<\/span> \u09ad\u09c7\u09a4\u09b0\u09c7\u09b0 \u09aa\u09bf\u09a0\u09c7\u09b0 \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7 <\/span>b<\/span> \u098f\u09ac\u0982 \u09ac\u09be\u0987\u09b0\u09c7\u09b0 \u09aa\u09bf\u09a0\u09c7\u09b0 \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7 <\/span>a<\/span>\u0964 <\/span>P<\/span> \u09b9\u09b2\u09cb \u09ac\u09be\u0987\u09b0\u09c7\u09b0 \u098f\u0995\u099f\u09bf \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1, \u09af\u0996\u09a8 <\/span>OP = r<\/span>\u0964 \u0997\u09cb\u09b2\u0995\u099f\u09bf\u0995\u09c7 \u0985\u09a8\u09c7\u0995\u0997\u09c1\u09b2\u09bf \u09b8\u09ae\u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0\u09bf\u0995 \u09b8\u09b0\u09c1 \u09ac\u09c7\u09a7\u09c7\u09b0 \u0996\u09cb\u09b2\u0995\u09c7\u09b0 \u09b8\u09ae\u09b7\u09cd\u099f\u09bf \u09ad\u09be\u09ac\u09be \u09af\u09c7\u09a4\u09c7 \u09aa\u09be\u09b0\u09c7\u0964 \u098f\u09b0\u0995\u09ae \u098f\u0995\u099f\u09bf \u0996\u09cb\u09b2\u0995 \u09a8\u09c7\u09af\u09bc\u09be \u09b9\u09b2\u09cb \u09af\u09be\u09b0 \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7 <\/span>x<\/span> \u098f\u09ac\u0982 \u09ac\u09c7\u09a7 dt <\/span><\/span>\u00a0\u0997\u09cb\u09b2\u0995\u09c7\u09b0 \u0989\u09aa\u09be\u09a6\u09be\u09a8\u09c7\u09b0 \u0998\u09a8\u09a4\u09cd\u09ac <\/span> \u09b9\u09b2\u09c7, \u09b8\u09b0\u09c1 \u09ac\u09c7\u09a7\u09c7\u09b0 \u0996\u09cb\u09b2\u0995\u09c7\u09b0 \u09ad\u09b0 <\/span>=4 \\pi x^{2} d x \\rho <\/span><\/span><\/p>\n

\u0989\u0995\u09cd\u09a4 \u0997\u09cb\u09b2\u0995\u09c7\u09b0 <\/span>P<\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09a6\u09b0\u09c1\u09a8 \u09ac\u09bf\u09ad\u09ac d V_{p} <\/span><\/span>=-G \\frac{\\text { \u0996\u09cb\u09b2\u0995\u09c7\u09b0 \u09ad\u09b0 }}{r}<\/span><\/span>=<\/span>-\\frac{-G 4 \\pi x^{2} d x \\rho}{r} <\/span><\/span><\/p>\n

\u2234\u00a0<\/span>\u09b8\u09ae\u0997\u09cd\u09b0 \u0997\u09cb\u09b2\u0995\u09c7\u09b0 \u09ac\u09bf\u09ad\u09ac<\/span> V_{p} <\/span><\/span>=-\\frac{4 \\pi G \\rho}{r} <\/span>\\int_{b}^{a} x^{2} d x <\/span><\/span>=\\frac{-4 \\pi G \\rho}{r} <\/span>\\frac{\\left(a^{3}-b^{3}\\right)}{3} <\/span>=\\frac{-G M}{r} <\/span><\/span><\/p>\n

\u0986\u09ac\u09be\u09b0 <\/span>P<\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0 \u09aa\u09cd\u09b0\u09be\u09ac\u09b2\u09cd\u09af \\left(V_{p}\\right)_{0} <\/span><\/span>=\\frac{d}{d r} <\/span>(\\frac{-G M}{r} <\/span>)<\/span>=\\frac{+G M}{r} <\/span><\/span><\/p>\n

\u09ab\u09be\u0981\u09aa\u09be \u0997\u09cb\u09b2\u0995\u09c7\u09b0 \u09ad\u09c7\u09a4\u09b0\u09c7 \u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7\u09c0\u09af\u09bc \u09b8\u09c2\u09a4\u09cd\u09b0\u09c7\u09b0 \u09ac\u09cd\u09af\u09ac\u09b9\u09be\u09b0 :\u09ac\u09bf\u09ad\u09ac \u0993 \u09aa\u09cd\u09b0\u09be\u09ac\u09b2\u09cd\u09af \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc\u00a0 (<\/b>Use of gravitational law inside the hollow sphere :Determination of potential and intensity)<\/b>\u00a0<\/b><\/h2>\n

\u09af\u0996\u09a8 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u099f\u09bf \u0997\u09cb\u09b2\u0995\u09c7\u09b0 \u09ad\u09c7\u09a4\u09b0 \u0985\u09ac\u09b8\u09cd\u09a5\u09bf\u09a4:<\/h3>\n

\"gravitational-law\"<\/p>\n

\u0997\u09cb\u09b2\u0995\u09c7\u09b0 \u09ad\u09c7\u09a4\u09b0 \u09ab\u09be\u0981\u09aa\u09be \u0985\u0982\u09b6\u09c7 <\/span>P<\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u09a8\u09c7\u09af\u09bc\u09be \u09b9\u09b2\u09cb \u0964 <\/span>OP =r <\/span><\/span>; <\/span>a<\/span> \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7\u09c7\u09b0 \u098f\u09ac\u0982 <\/span>dx <\/span><\/span> \u09ac\u09c7\u09a7\u09c7\u09b0 \u098f\u0995\u099f\u09bf \u09aa\u09be\u09a4\u09b2\u09be \u0996\u09cb\u09b2\u0995 \u09a8\u09c7\u09af\u09bc\u09be \u09b9\u09b2\u09cb\u0964 \u0997\u09cb\u09b2\u0995\u099f\u09bf\u09b0 \u09ad\u09b0 <\/span>=4 \\pi x^{2} d x \\rho <\/span><\/span><\/p>\n

\u0989\u0995\u09cd\u09a4 \u0996\u09cb\u09b2\u0995\u09c7\u09b0 P \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09a6\u09b0\u09c1\u09a8 \u09ac\u09bf\u09ad\u09ac d V_{p} <\/span><\/span>=-G\\frac{\\text { \u0996\u09cb\u09b2\u0995\u09c7\u09b0 \u09ad\u09b0 }}{x} <\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>=-G <\/span>\\frac{4 \\pi x^{2} d x \\rho}{x} <\/span><\/span>=-4 \\pi G \\rho x d x <\/span><\/span><\/p>\n

\u0995\u09be\u09b0\u09a3 \u0996\u09cb\u09b2\u0995\u09c7\u09b0 \u09ab\u09be\u0981\u09aa\u09be \u0985\u0982\u09b6\u09c7\u09b0 \u09ad\u09c7\u09a4\u09b0 \u09ac\u09bf\u09ad\u09ac \u09b8\u09b0\u09cd\u09ac\u09a4\u09cd\u09b0 \u09b8\u09ae\u09be\u09a8 \u098f\u09ac\u0982 \u09af\u09be\u09b0 \u09ae\u09be\u09a8 <\/span>=-G\\frac{\u0996\u09cb\u09b2\u0995\u09c7\u09b0 \u09ad\u09b0} {\u0996\u09cb\u09b2\u0995\u09c7\u09b0 \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7 } <\/span><\/span>\u00a0<\/span><\/p>\n

\u09a4\u09be\u09b9\u09b2\u09c7, \u09b8\u09ae\u0997\u09cd\u09b0 \u0997\u09cb\u09b2\u0995\u09c7\u09b0 \u09a6\u09b0\u09c1\u09a8 \u09ac\u09bf\u09ad\u09ac,\u00a0<\/span><\/p>\n

d V_{p} <\/span>=-4 \\pi G \\rho <\/span>\\int_{b}^{a} x d x <\/span><\/span>=-2 \\pi G \\rho <\/span><\/span><\/p>\n

\u098f\u09ac\u0982 \u09aa\u09cd\u09b0\u09be\u09ac\u09b2\u09cd\u09af, d E_{p} <\/span><\/span>=+\\frac{d V_{p}}{d r} <\/span><\/span>=0<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

\u09a8\u09bf\u09b0\u09c7\u099f \u0997\u09cb\u09b2\u0995\u09c7\u09b0 \u0985\u09ad\u09cd\u09af\u09a8\u09cd\u09a4\u09b0\u09c7 \u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7\u09c0\u09af\u09bc \u09b8\u09c2\u09a4\u09cd\u09b0\u09c7\u09b0 \u09ac\u09cd\u09af\u09ac\u09b9\u09be\u09b0 :\u09ac\u09bf\u09ad\u09ac \u0993 \u09aa\u09cd\u09b0\u09be\u09ac\u09b2\u09cd\u09af \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc\u00a0 (Uses of Gravitational law inside a solid sphere :Determination of potential and intensity)\u00a0 \u00a0\u09af\u0996\u09a8 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u099f\u09bf \u0997\u09cb\u09b2\u0995\u09c7\u09b0 \u09ad\u09c7\u09a4\u09b0 \u0985\u09ac\u09b8\u09cd\u09a5\u09bf\u09a4:\u00a0 \u09ae\u09a8\u09c7 \u0995\u09b0\u09bf P \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u099f\u09bf \u0997\u09cb\u09b2\u0995\u09c7\u09b0 \u0989\u09aa\u09be\u09a6\u09be\u09a8\u09c7\u09b0 \u09ad\u09c7\u09a4\u09b0 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0 \u09b9\u09a4\u09c7 \u09a6\u09c2\u09b0\u09c7 \u0985\u09ac\u09b8\u09cd\u09a5\u09bf\u09a4 \u0964<\/p>\n

Read More<\/a><\/p>\n","protected":false},"author":56,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[4240,3028,50,51],"tags":[2788,2789,2786,2787],"_links":{"self":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/4124"}],"collection":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/users\/56"}],"replies":[{"embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/comments?post=4124"}],"version-history":[{"count":24,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/4124\/revisions"}],"predecessor-version":[{"id":12348,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/4124\/revisions\/12348"}],"wp:attachment":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/media?parent=4124"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/categories?post=4124"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/tags?post=4124"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}